HERE'S HOW
Put a raw egg (in its shell) into a bowl and cover it completely with vinegar.
Wait two days, then drain off the vinegar. When you touch the egg, it will feel rubbery. Be careful not to break the membrane, and wash your hands after you touch the egg. (Throw it away after a few days.)

WHY?
Vinegar, an acid, dissolves the calcium in the eggshell. It's calcium that makes the shell hard. But a thin, flexible membrane just under the shell still holds the egg's shape.